Fixed point theory
-24. Common fixed point results for graph preserving mappings in parametric $N_b$-metric spaces

S. Kumar Mohanta; R. Kar

Volume 09, Issue 02 , Spring 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

Operator theory
-23. 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 , Spring 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
-22. Fixed point results for Su-type contractive mappings with an application

A. Ali; H. Işık; F. Uddin; M. Arshad

Volume 09, Issue 01 , Winter 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

Several complex variables and analytic spaces
-21. Multi-valued fixed point theorems in complex valued $b$-metric spaces

F. Ahmad; M. ‎Shehu Shagari; A. Azam

Volume 09, Issue 01 , Winter 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
-20. $C$-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 , Autumn 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
-19. $(F,\varphi‎ ,‎\alpha )_{s}$-contractions in ‎$‎b‎$‎-metric spaces and applications

M. Sangurlu Sezen

Volume 08, Issue 03 , Summer 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
-18. Generalized hyperstability of the cubic functional equation in ultrametric spaces

Y. ‎Aribou; H. Dimou; S. Kabbaj

Volume 08, Issue 02 , Spring 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
-17. Suzuki-Berinde type fixed-point and fixed-circle results on $S$-metric spaces

N. TAŞ

Volume 07, Issue 03 , Summer 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
-16. Fixed point theorem for mappings satisfying contractive condition of integral type on intuitionistic fuzzy metric space

M. E. Samei

Volume 07, Issue 03 , Summer 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
-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 , Summer 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
-14. Existence of best proximity and fixed points in $G_p$-metric spaces

S. Rathee; K. Dhingra

Volume 07, Issue 03 , Summer 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
-13. 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 , Summer 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
-12. Some fixed point results for contractive type mappings in b-metric spaces

I. Eroğlu

Volume 07, Issue 03 , Summer 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
-11. $ b-(\varphi, \Gamma)-$graphic contraction on metric space endowed with a graph

Sh. Mirzaee; M. Eshaghi Gordji

Volume 07, Issue 03 , Summer 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
-10. Fixed points of weak $\psi$-quasi contractions in generalized metric spaces

K. P. R. Sastry; G. V. R. Babu; P. S. Kumar

Volume 06, Issue 04 , Autumn 2017, , Pages 323-329

Abstract
  In this paper, we introduce the notion of weak $\psi$-quasi contraction in generalized metric spaces and using this notion we obtain conditions for the existence of fixed points of a self map in $D$-complete generalized metric spaces. We deduce some corollaries from our result and provide examples in ...  Read More

Fixed point theory
-9. A fixed point method for proving the stability of ring $(\alpha, \beta, \gamma)$-derivations in $2$-Banach algebras

M. Eshaghi Gordji; S. Abbaszadeh

Volume 06, Issue 04 , Autumn 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
-8. A solution of nonlinear fractional random differential equation via random fixed point technique

R. A. Rashwan; H. A. Hammad

Volume 06, Issue 04 , Autumn 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
-7. On some open problems in cone metric space over Banach algebra

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

Volume 06, Issue 04 , Autumn 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
-6. Common best proximity points for $(\psi-\phi)$-generalized weak proximal contraction type mappings

K. K. M. Sarma; G. Yohannes

Volume 06, Issue 04 , Autumn 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
-5. 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 , Autumn 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

Fixed point theory
-4. Fixed point theory in generalized orthogonal metric space

M. Eshaghi Gordji; H. Habibi

Volume 06, Issue 03 , Summer 2017, , Pages 251-260

Abstract
  In this paper, among the other things, we prove the existence and uniqueness theorem of fixed point for mappings on a generalized orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point of Cauchy problem for the first order differential equation.  Read More

Fixed point theory
-3. Unique common coupled fixed point theorem for four maps in $S_b$-metric spaces

K. P. R. Rao; G. V. N. Kishore; Sk. Sadik

Volume 06, Issue 01 , Winter 2017, , Pages 29-43

Abstract
  In this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $S_b$-metric spaces satisfying a contrctive type condition. We furnish an example to support our main theorem. We also give a corollary for Junck type maps.  Read More

Approximations and expansions
-2. New best proximity point results in G-metric space

A. H. Ansari; A. Razani; N. Hussain

Volume 06, Issue 01 , Winter 2017, , Pages 73-89

Abstract
  Best approximation results provide an approximate solution to the fixed point equation $Tx=x$, when the non-self mapping $T$ has no fixed point. In particular, a well-known best approximation theorem, due to Fan cite{5}, asserts that if $K$ is a nonempty compact convex subset of a Hausdorff locally ...  Read More

Fixed point theory
-1. Coupled fixed point theorems involving contractive condition of integral type in generalized metric spaces

R. Shah; A. Zada

Volume 06, Issue 01 , Winter 2017, , Pages 45-53

Abstract
  In this manuscript, we prove some coupled fixed point theorems for two pairs of self mappings satisfying contractive conditions of integral type in generalized metric spaces. We furnish suitable illustrative examples. In this manuscript, we prove some coupled fixed point theorems for ...  Read More

Integral equations
0. Random fixed point theorems with an application to a random nonlinear integral equation

R. A. Rashwan; H. A. Hammad

Volume 05, Issue 02 , Spring 2016, , Pages 119-133

Abstract
  In this paper, stochastic generalizations of some fixed point for operators satisfying random contractively generalized hybrid and some other contractive condition have been proved. We discuss also the existence of a solution to a nonlinear random integral equation in Banah spaces.  Read More