‎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 to‎ ‎validate our main result and a non-trivial example is given to‎ ‎elucidate our work.

In this paper, we prove the ∆-convergence theorems of the cyclic algorithm and the new multi-step iteration for k-strictly pseudo-contractive mappings and give also the strong convergence theorem of the modified Halpern’s iteration for these mappings in a CAT (0) space. Our results extend and improve the corresponding recent results announced by many authors in the literature. Key–Words: CAT (0...

Very recently, Agarwal et al. (Fixed Point Theory Appl. 2012:40, 2012) initiated the study of fixed point theorems for mappings satisfying cyclical generalized contractive conditions in complete partial metric spaces. In the present paper, we study some fixed point theorems for a mapping satisfying a cyclical generalized contractive condition based on a pair of altering distance functions in co...

Fixed point results for a self-map satisfying locally contractive conditions on a closed ball in an ordered 0-complete quasi-partial metric space have been established. Instead of monotone mapping, the notion of dominated mappings is applied. We have used weaker metric, weaker contractive conditions, and weaker restrictions to obtain unique fixed points. An example is given which shows that how...

It is well known that the classical contraction mapping principle of Banach is a fundamental result in fixed point theory. Several authors have obtained various extensions and generalizations of Banach’s theorems by considering contractive mappings on different metric spaces. Huang and Zhang [1] have replaced real numbers by ordering Banach space and have defined a cone metric space. They have ...

Abstract In the present paper concepts of q-rung orthopair fuzzy mappings (q-ROF mapping) and $( \alpha ,\beta ) $ ( α , β ) -cuts are introduced. Some common fixed point results for q-ROF presented in b-metric spaces using Suzuki-type contra...

Let E be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of E has the fixed point property for nonexpansive mappings. Let C be a nonempty closed convex subset of E, f : C → C a contractive mapping or a weakly contractive mapping , and T : C → C nonexpansive mapping with the fixed point set F T / ∅. Let {xn} be generated by a...

We use the fixed point method to prove the probabilistic Hyers–Ulam and generalized Hyers–Ulam–Rassias stability for the nonlinear equation f (x) = Φ(x, f (η(x))) where the unknown is a mapping f from a nonempty set S to a probabilistic metric space (X ,F,TM) and Φ : S×X → X , η : S → X are two given functions. Mathematics subject classification (2000): 39B52, 39B82, 47H10, 54E70.

The purpose of this article is to investigate common solutions of a zero point problem of a accretive operator and a fixed point problem of a nonexpansive mapping via a viscosity approximation method involving a τ-contractive mapping. c ©2017 All rights reserved.

Optimal Reactive Power Dispatch (ORPD) is a multi-variable problem with nonlinear constraints and continuous/discrete decision variables. Due to the stochastic behavior of loads, the ORPD requires a probabilistic mathematical model. In this paper, Monte Carlo Simulation (MCS) is used for modeling of load uncertainties in the ORPD problem. The problem is formulated as a nonlinear constrained mul...