##### Volume 01 (2012)
Fixed point theory
##### 1. The triples of $(v,u,\phi)$-contraction and $(q,p,\phi)$-contraction in $b$-metric spaces and its application

Volume 11, Issue 01 , March 2022, , Pages 39-46
##### Abstract
‎The aim of this work is to introduce the concepts of $(v‎, ‎u‎, ‎\phi)$-contraction and $(q‎, ‎p‎, ‎\phi)$-contraction‎, ‎and to obtain new results in fixed point theory for four mappings in $b$-metric spaces‎. ‎Finally‎, ‎we have developed ...  Read More

Fixed point theory
##### 2. $b$-metric spaces with a graph and best proximity points for some contractions

K. Fallahi; M. Ayobian

Volume 10, Issue 04 , December 2021, , Pages 277-286

##### Abstract
In this paper, we introduce a new type of graph contraction using a special class of functions and give a best proximity point theorem for this contraction in complete metric spaces endowed with a graph. Then we support our main theorem by a non-trivial example and give some consequences of it for usual ...  Read More

Fixed point theory
##### 3. Coincident and common fixed point theorems using comparison and admissible function in w-distance metric space

S. Arora; M. Masta

Volume 10, Issue 04 , December 2021, , Pages 323-333

##### Abstract
‎In this manuscript‎, ‎the concept of generalized $(\eta‎, ‎\chi‎, ‎p)$ contractive mapping for two maps in the framework of w-distance is introduced and some fixed point results are established, which extend recent results of Lakzian and Rhoades [5] and many existing results ...  Read More

Functional analysis
##### 4. Hybrid linesearch algorithm for pseudomonotone equilibrium problem and fixed points of Bregman quasi asymptotically nonexpansive multivalued mappings

M. H. Harbau; B. Ali

Volume 10, Issue 02 , June 2021, , Pages 153-177

##### Abstract
In this paper, we introduce a linesearch algorithm for solving fixed points of Bregman quasi asymptotically nonexpansive multivalued mappings and pseudomonotone equilibrium problem in reflexive Banach space. Using the linesearch method, we prove a strong convergence of the iterative scheme to a common ...  Read More

Operator theory
##### 5. Coupled fixed point results for $T$-contractions on $\mathcal{F}$-metric spaces and an application

Volume 10, Issue 01 , March 2021, , Pages 1-10

##### Abstract
The main purpose of this article is to introduce the concept of $T$-contraction type mappings in the function weighed metric spaces and to obtain some coupled fixed points theorems in this framework. Also, an example and an application of the existence of a solution of a system of nonlinear integral ...  Read More

Fixed point theory
##### 6. $S$-metric and fixed point theorem

M. Simkhah Asil; Sh. Sedghi; N. Shobe; Z. Mitrovic

Volume 09, Issue 03 , September 2020, , Pages 213-220

##### Abstract
In this paper, we prove a general fixed point theorem in $\textrm{S}$-metric spaces for maps satisfying an implicit relation on complete metric spaces. As applications, we get many analogues of fixed point theorems in metric spaces for $\textrm{S}$-metric spaces.  Read More

Operator theory
##### 7. Integral type contraction and coupled fixed point theorems in ordered G-metric spaces

E. Lotfali Ghasab; H. Majani; G. Soleimani Rad

Volume 09, Issue 02 , June 2020, , Pages 113-120

##### Abstract
In this paper, we apply the idea of integral type contraction and prove some coupled fixed point theorems for such contractions in ordered $G$-metric space. Also, we support the main results by an illustrative example.  Read More

Fixed point theory
##### 8. Common fixed point results for graph preserving mappings in parametric $N_b$-metric spaces

S. Kumar Mohanta; R. Kar

Volume 09, Issue 02 , June 2020, , Pages 165-183

##### Abstract
In this paper, we discuss the existence and uniqueness of points of coincidence and common fixed points for a pair of graph preserving mappings in parametric $N_b$-metric spaces. As some consequences of this study, we obtain several important results in parametric $b$-metric spaces, parametric $S$-metric ...  Read More

Fixed point theory
##### 9. Fixed point results for Su-type contractive mappings with an application

A. Ali; H. Işık; F. Uddin; M. Arshad

Volume 09, Issue 01 , March 2020, , Pages 53-65

##### Abstract
‎In this paper‎, ‎we introduce the concept of Su-type contractive mapping and establish fixed point theorems for such mappings in the setting of ordered‎ ‎extended partial $b$-metric space‎. ‎We also develop an‎ ‎application for Fredholm type integral equations ...  Read More

Fixed point theory
##### 10. Multi-valued fixed point theorems in complex valued $b$-metric spaces

F. Ahmad; M. ‎Shehu Shagari; A. Azam

Volume 09, Issue 01 , March 2020, , Pages 75-94

##### Abstract
‎The aim of this paper is to establish and prove some results on common fixed point‎ for a pair of multi-valued mappings in complex valued $b$-metric spaces‎. ‎Our‎ ‎results generalize and extend a few results in the literature‎.    Read More

Operator theory
##### 11. $C$-class functions on common fixed point theorems for weak‎ ‎contraction mapping of integral type in modular spaces

H. A. Hammad; R. A. Rashwan; A. H. Ansari

Volume 08, Issue 04 , December 2019, , Pages 265-285

##### Abstract
‎In this paper‎, ‎we use the concept of $C$-class functions introduced‎ ‎by Ansari [4] to prove the existence and uniqueness of‎ ‎common fixed point for self-mappings in modular spaces of integral‎ ‎inequality‎. ‎Our results extended and generalized ...  Read More

Fixed point theory
##### 12. $(F,\varphi‎ ,‎\alpha )_{s}$-contractions in ‎$‎b‎$‎-metric spaces and applications

M. Sangurlu Sezen

Volume 08, Issue 03 , August 2019, , Pages 173-182

##### Abstract
‎In this paper‎, ‎we introduce more general contractions called $\varphi$-fixed‎ ‎point point for $(F,\varphi‎ ,‎\alpha )_{s}$ and $(F,\varphi‎ ,‎\alpha )_{s}$-‎weak contractions‎. ‎We prove the existence and uniqueness of $\varphi$-‎fixed point ...  Read More

Fixed point theory
##### 13. Generalized hyperstability of the cubic functional equation in ultrametric spaces

Y. ‎Aribou; H. Dimou; S. Kabbaj

Volume 08, Issue 02 , June 2019, , Pages 97-104

##### Abstract
‎In this paper‎, ‎we present the‎ generalized hyperstability results of cubic functional equation in‎ ‎ultrametric Banach spaces using the fixed point method‎.  Read More

Fixed point theory
##### 14. Existence of best proximity and fixed points in $G_p$-metric spaces

S. Rathee; K. Dhingra

Volume 07, Issue 03 , September 2018, , Pages 155-168

##### Abstract
In this paper, we establish some best proximity point theorems using new proximal contractive mappings in asymmetric $G_{p}$-metric spaces. Our motive is to find an optimal approximate solution of a fixed point equation. We provide best proximity points for cyclic contractive mappings in $G_{p}$-metric ...  Read More

Fixed point theory
##### 15. Some local fixed point results under $C$-class functions with applications to coupled elliptic systems

A. Hojat Ansari; A. Benterki; M. Rouaki

Volume 07, Issue 03 , September 2018, , Pages 169-182

##### Abstract
The main objective of the paper is to state newly fixed point theorems for set-valued mappings in the framework of 0-complete partial metric spaces which speak about a location of a fixed point with respect to an initial value of the set-valued mapping by using some $C$-class functions. The results proved ...  Read More

Fixed point theory
##### 16. Fixed point theorem for mappings satisfying contractive condition of integral type on intuitionistic fuzzy metric space

M. E. Samei

Volume 07, Issue 03 , September 2018, , Pages 183-199

##### Abstract
In this paper, we shall establish some fixed point theorems for mappings with the contractive  condition of integrable type on complete intuitionistic fuzzy metric spaces $(X, M,N,*,\lozenge)$. We also use Lebesgue-integrable mapping to obtain new results. Akram, Zafar, and Siddiqui introduced the ...  Read More

Fixed point theory
##### 17. Common fixed points for a pair of mappings in $b$-Metric spaces via digraphs and altering distance functions

S. K. Mohanta; D. Biswas

Volume 07, Issue 03 , September 2018, , Pages 201-218

##### Abstract
In this paper, we discuss the existence and uniqueness of points of coincidence and common fixed points for a pair of self-mappings satisfying some generalized contractive type conditions in $b$-metric spaces endowed with graphs and altering distance functions. Finally, some examples are provided ...  Read More

Fixed point theory
##### 18. Some fixed point results for contractive type mappings in b-metric spaces

I. Eroğlu

Volume 07, Issue 03 , September 2018, , Pages 219-231

##### Abstract
In this work, we prove some fixed point theorems by using $wt$-distance on b-metric spaces. Our results generalize some fixed point theorems in the literature. Moreover, we introduce $wt_0$-distance and by using the concept of $wt_0$-distance, we obtain some coupled fixed point results in complete b-metric ...  Read More

Fixed point theory
##### 19. Suzuki-Berinde type fixed-point and fixed-circle results on $S$-metric spaces

N. TAŞ

Volume 07, Issue 03 , September 2018, , Pages 233-244

##### Abstract
In this paper, the notions of a Suzuki-Berinde type $F_{S}$-contraction and a Suzuki-Berinde type $F_{C}^{S}$-contraction are introduced on a $S$-metric space. Using these new notions, a fixed-point theorem is proved on a complete $S$-metric space and a fixed-circle theorem is established on ...  Read More

Fixed point theory
##### 20. $b-(\varphi, \Gamma)-$graphic contraction on metric space endowed with a graph

Sh. Mirzaee; M. Eshaghi Gordji

Volume 07, Issue 03 , September 2018, , Pages 245-250

##### Abstract
In this paper, we introduce the $b-(\varphi, \Gamma)-$graphic contraction on metric space endowed with a graph so that $(M,\delta)$ is a metric space, and $V(\Gamma)$ is the vertices of $\Gamma$ coincides with $M$. We aim to obtain some new fixed-point results for such contractions. We give an example ...  Read More

Fixed point theory
##### 21. On some open problems in cone metric space over Banach algebra

A. Ahmed; Z. D. Mitrovic; J. N. Salunke

Volume 06, Issue 04 , December 2017, , Pages 261-267

##### Abstract
In this paper we prove an analogue of Banach and Kannan fixed point theorems by generalizing the Lipschitz constat $k$, in generalized Lipschitz mapping on cone metric space over Banach algebra, which are answers for the open problems proposed by Sastry et al, [K. P. R. Sastry, G. A. Naidu, T. Bakeshie, ...  Read More

Fixed point theory
##### 22. A fixed point method for proving the stability of ring $(\alpha, \beta, \gamma)$-derivations in $2$-Banach algebras

Volume 06, Issue 04 , December 2017, , Pages 269-276

##### Abstract
In this paper, we first present the new concept of $2$-normed algebra. We investigate the structure of this algebra and give some examples. Then we apply a fixed point theorem to prove the stability and hyperstability of $(\alpha, \beta, \gamma)$-derivations in $2$-Banach algebras.  Read More

Fixed point theory
##### 23. A solution of nonlinear fractional random differential equation via random ﬁxed point technique

R. A. Rashwan; H. A. Hammad

Volume 06, Issue 04 , December 2017, , Pages 277-287

##### Abstract
In this paper, we investigate a new type of random $F$-contraction and obtain a common random fixed point theorem for a pair of self stochastic mappings in a separable Banach space. The existence of a unique solution for nonlinear fractional random differential equation is proved under suitable conditions.  Read More

Fixed point theory
##### 24. Common best proximity points for $(\psi-\phi)$-generalized weak proximal contraction type mappings

K. K. M. Sarma; G. Yohannes

Volume 06, Issue 04 , December 2017, , Pages 289-300

##### Abstract
In this paper, we introduce a pair of generalized proximal contraction mappings and prove the existence of a unique best proximity point for such mappings in a complete metric space. We provide examples to illustrate our result. Our result extends some of the results in the literature.  Read More

Fixed point theory
##### 25. Coincidence points and common fixed points for hybrid pair of mappings in b-metric spaces endowed with a graph

S. K. Mohanta; S. Patra

Volume 06, Issue 04 , December 2017, , Pages 301-321

##### Abstract
In this paper, we introduce the notion of strictly (α,ψ,ξ)-G-contractive mappings in b-metric spaces endowed with a graph G. We establish a sufficient condition for existence and uniqueness of points of coincidence and common fixed points for such mappings. Our results extend and unify many ...  Read More