Solutions of Integral Equations via Fixed-Point Results on Orthogonal Gauge Structure

Abstract

The main outcome of this paper is to introduce the notion of orthogonal gauge spaces and to present some related fixed-point results. As an application of our results, we obtain existence theorems for integral equations.

On Fuzzy Fixed-Point Results in Complex Valued Extended b-Metric Spaces with Application

“…In 2011, Azam et al [7] introduced the concept of complex valued metric space and obtained some common fixed-point results for rational contraction which consist of a pair of single valued mappings. Later on, many researchers [8][9][10][11][12][13][14][15] worked on this generalized metric space. Ahmad et al [16] and Azam et al [17] defined the generalized Housdorff metric function in the setting of complex valued metric space and obtained common fixed-point results for multivalued mappings.…”

Some fixed point theorems on orthogonal metric spaces via extensions of orthogonal contractions

“…This gracious theorem has been used to show the presence and uniqueness of the solution of differantial equation y ′ (x) = F (x; y); y(x 0 ) = y 0 (2) where F is a continuously differantiable function. Consequently, after the Banach Contraction Principle on complete metric space, many researchers have investigated for anymore fixed point results and reported 482 N. BILGILI GUNGOR new fixed point theorems intended by the use of two very influential directions, assembled or apart ( See [2], [4], [5], [6], [7], [8], [9], [10], [11], [16], [17], [18]). One of them is involved with the attempts to generalize the contractive conditions on the maps and thus, soften them; the other with to attempts to generalize the space on which these contractions are described.…”