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A Fixed point Theorem Satisfying Integral Type Contraction in Fuzzy Metric Space -by Sharafat Hussain and Maria Samreen

Abstract: In this paper we analyze the existence of fixed points for mappings defined on a complete fuzzy metric space satisfying a contractive condition of integral type. Our main result generalize the fuzzy Banach contraction theorem of V. Gregori and A. Sapena [V. Gregori and A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy…

Fixed points of sequences of mappings -by C. Ganesa Moorthy and S. Iruthaya Raj

Abstract: The concept of fixed points of a mapping is known. A new concept of fixed points of a sequence of mappings is introduced. Some results that are similar to the Banach contraction principle are obtained. A result for asymptotically nonexpansive type mappings is also obtained. Keywords: Fixed point, semi metric, Hausdorff metric. DOI: https://doi.org/10.30697/rfpta-2018-007 ______…

Fixed point theorems with cyclical contractive conditions in $b$-Menger spaces -by Abderrahim Mbarki and Rachid Oubrahim

Abstract: In this work, we prove a fixed point theorems in $b$-Menger spaces (Mbarki et al., Probabilistic $b$-metric spaces and nonlinear contractions, Fixed Point Theory Appl.  2017, Paper No. 29, 15 p. (2017)) using probabilistic contraction [1] with cyclical conditions. We support our results by an example. Keywords: $b$-Menger space, Fixed point, Cyclic probabilistic contraction. DOI: https://doi.org/10.30697/rfpta-2018-005…

Fixed point theorems of $C$-class functions in $S_{b}$-metric space -by D. Dhamodharan, Yumnam Rohen and A H Ansari

Abstract: In this paper, we use $C$-class function in order to obtain some coupled fixed point theorems in the setting of $S_{b}$-metric space. Some results are also given in the form of corollaries. Examples are also given to verify our results. Keywords: Coupled fixed point,$S_b$ metric space and $C$-class function. DOI: https://doi.org/10.30697/rfpta-2018-018 ______ How to cite this…

Coupled fixed point theorems for generalized contractions in ordered $M$-metric spaces -by Hossein Monfared, Mehdi Asadi and Mahdi Azhini

Abstract: Using control functions, we improve and extend some results of coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces by Lakshmikantam and $\acute{C}$iri$\acute{c}$ [24] to ordered $M$-metric spaces. Keywords: Fixed point; Partial metric space; $M$-metric space; Coupled fixed point. DOI: https://doi.org/10.30697/rfpta-2018-004 ______ How to cite this article: H. Monfared, M. Asadi, M. Azhini,…

Parallel extragradient-proximal methods for solving split system of fixed point set constraint equilibrium problem in real Hilbert space -by Anteneh Getachew Gebrie and Rabian Wangkeeree

Abstract: In this paper, we propose two parallel extragradient-proximal methods for solving finite family of split equilibrium problems and split common fixed point problems, we call the problem split system of fixed point set constraint equilibrium problem (SSFPSCEP). The algorithms combine the extragradient method, the proximal method and the shrinking projection method. The weak and…

Variational Relations in Abstract Convex Spaces -by Sehie Park

Abstract: Luc [1] initiated the study of variational relations, which is a unifying approach to various models of equilibrium theory and variational inclusions. There, a simple condition was established for the existence of solutions of variational relations and was applied to a number of variational problems. In the present article, certain results in [1] are…

Layered Compression-Expansion Fixed Point Theorem -by Richard I. Avery, Douglas R. Anderson and Johnny Henderson

Abstract: The layered compression-expansion fixed point theorem is an alternative approach to the Krasnoselskii fixed point theorem for perturbed operators. The layered compression-expansion fixed point theorem is used to verify the existence of a fixed point to an operator of the form $T = R+S$ (sum of operators) by verifying the existence of a fixed…

On the qualitative properties of functional integral equations with abstract Volterra operators -by Diana Otrocol and Veronica Ilea

Abstract: Using the weakly Picard operators technique we establish existence, data dependence and comparison results of solutions for a functional integral equation with abstract Volterra operators. Some examples which show the importance of our results are also included. Keywords: Functional integral equation, weakly Picard operators, data dependence and abstract Volterra operator. DOI: https://doi.org/10.30697/rfpta-2018-13 ______ How to…

Comments on some Fixed Point Theorems -by B. E. Rhoades

Abstract: The purpose of this paper is to show that a number of fixed point theorems are special cases of two theorems of Jungck and the author [6]. Keywords: Fixed point theorem, $G$-metric space, occasionally weakly compatible. DOI: https://doi.org/10.30697/rfpta-2018-001 ______ How to cite this article: B. E. Rhoades, Comments on some Fixed Point Theorems, Results in Fixed Point Theory…