F-Convex Contraction via Admissible Mapping and Related Fixed Point Theorems with an Application

Abstract

Abstract:In this paper, we introduce F-convex contraction via admissible mapping in the sense of Wardowski [Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl., 94 (2012), 6 pages] which extends convex contraction mapping of type-2 of Istrǎţescu [Some fixed point theorems for convex contraction mappings and convex non-expansive mappings (I), Libertas Mathematica, 1(1981), 151-163] and establish a fixed point theorem in the setting of metric space. Our result extends and generalizes some other similar results in the literature. As an application of our main result, we establish an existence theorem for the non-linear Fredholm integral equation and give a numerical example to validate the application of our obtained result.

Alpha- F -Convex Contraction Mappings in b -Metric Space and a Related Fixed Point Theorem

“…Definition 2 (see [11]). An α-admissible mapping T is said to be α * -admissible, if for each x, y ∈ FixðTÞ ≠ ∅, we have αðx, yÞ ≥ 1: If FixðTÞ = ∅, we say that T is vacuously α * -admissible.…”

“…Istratescu [2] introduced a class of convex contraction mappings in metric spaces and generalized the well-known Banach contraction principle. Afterwards, some works have appeared on the generalization of such classes of mappings in the setting of various spaces [3][4][5][6][7][8][9][10][11][12]. We focus on the research works of Eke et al [5] for our purpose.…”

Correction: Singh, Y. Mahendra, et al. F-Convex Contraction via Admissible Mapping and Related Fixed Point Theorems with an Application. Mathematics 2018, 6, 105

“…In the proof of the Theorem 2 [1], instead of the following: "By Lemma 1, {d p (x n , x n+1 )} is strictly non-increasing sequence. Therefore,…”

“…We found some errors in Lemma 1 of our paper [1], thus, we would like to make the following corrections:…”

Operators of Fractional Calculus and Their Applications

“…Website: http://www.math.uvic.ca/faculty/harimsri/ This volume contains the successfully invited and accepted submissions (see [1][2][3][4][5][6][7][8][9]) to a Special Issue of MDPI's journal, Mathematics in the subject area of "Operators of Fractional Calculus and Their Applications".…”