A fixed point theorem on multiplicative metric space with integral-type inequality

Abstract

In this paper, we prove fixed point theorems (FPTs) on multiplicative metric space (MMS) (X, ) by the help of integral-type contractions of self-quadruple mappings (SQMs), i.e., for ℘ 1 , ℘ 2 , ℘ 3 , ℘ 4 : X → R. For this, we assume that the SQMs are weakly compatible mappings and the pairs ℘ 1 , ℘ 3 and ℘ 2 , ℘ 4 satisfy the property (CLR ℘ 3 ℘ 4 ). Further, two corollaries are produced from our main theorem as special cases. The novelty of these results is that for the unique common fixed point (CFP) of the SQMs ℘ 1 , ℘ 2 , ℘ 3 , ℘ 4 , we do not need to the assumption of completeness of the MMS (X, ). These results generalize the work of Abdou, [A. A. N. Abdou, J. Nonlinear Sci. Appl., 9 (2016), 2244-2257, and many others in the available literature.

Fixed Point Results on Generalized Multiplicative Contraction Mappings in Extended b-Multiplicative Metric Spaces

“…Some authors have contributed to the use of the multiplicative metric space for fixed point results such as by Abbas et al (2015) and Abdou (2016). Similarly, Khan et al (2017) used the space for fixed point results on integral-type inequality and Singh et al (2016) proposed and proved fixed point theorems on expansive mapping. However, some researchers utilized the space for common fixed point results on multiplicative contraction such as He et al (2014) who proved common fixed point theorems on weak commutative mapping and Gu and Cho (2015) who proved common fixed point theorems of four maps on multiplicative contraction mapping.…”

A generalization of Minkowski’s inequality by Hahn integral operator

“…One of the aspects which are nowadays very much popular among the scientists for research is the integral inequalities with applications. In this area, most of the authors are generalizing the standard results in the available literature by using different types/definitions of the fractional integral operators (FIOs) [1][2][3][4][5][6][7][8][9].…”

“…For instance, Khan et al [1] studied an integral inequality for a class of decreasing n positive functions where n ∈ N for the left-and right-fractional conformable integrals. Khan et al [2] considered new fixed point theorems by the help of integral inequalities for a class of quadruple self-mappings. Chen and Katugampola [3] obtained fractional integral inequalities called Hermite-Hadamard and Hermite-Hadamard-Fejér which generalize the classical cases.…”