Turkish Journal of Analysis and Number Theory, 2018, Vol. 6, No. 6, 159-163 Available online at http://pubs.sciepub.com/tjant/6/6/3 ©Science and Education Publishing DOI:10.12691/tjant-6-6-3 Fixed Point Results in JS-Multiplicative Metric Spaces Abdullah Shoaib * , Qaiser Mehmood Department of Mathematics and Statistics, Riphah International University, Islamabad - 44000, Pakistan *Corresponding author: abdullahshoaib15@yahoo.com Received September 22, 2018; Revised November 11, 2018; Accepted December 06, 2018 Abstract In this paper, we have introduced JS-multiplicative metric space and proved some fixed point theorems in this space. This new metric function is a generalized form of several functions such as multiplicative metric, dislocated multiplicative metric, multiplicative b-metric and multiplicative b-metric-like. Keywords: fixed point, Js multiplicative metric space, multiplicative metric space, multiplicative b-metric-like space, multiplicative b-metric space 2010 Mathematics Subject Classification: 46S40; 47H10; 54H25. Cite This Article: Abdullah Shoaib, and Qaiser Mehmood, “Fixed Point Results in JS-Multiplicative Metric Spaces.” Turkish Journal of Analysis and Number Theory, vol. 6, no. 6 (2018): 159-163. doi: 10.12691/tjant-6-6-3. 1. Introduction Ozaksar and Cevical [1] investigated multiplicative metric space and proved its topological properties. Mongkolkeha et al. [2] described the concept of multiplicative proximal contraction mapping and proved best proximity point theorems for such mappings. Recently, Abbas et al. [3] proved some common fixed point results of quasi weak commutative mappings on a closed ball in the setting of multiplicative metric spaces. They also describe the main conditions for the existence of common solution of multiplicative boundary value problem. For further results on multiplicative metric space, see [4,5,6,7]. In 2017, Ali et al. [8] introduced the notion of b -multiplicative and proved some fixed point result. As an application, they established an existence theorem for the solution of a system of Fredholm multiplicative integral equations. Bakht Zada and Usman Riaz [9] introduced the idea of multiplicative b-metric-like space. Jleli and Samet [10] introduce a new generalization of metric space called generalized metric space (Js-metric space) and proved some fixed point theorems (see [11,12,13] for further results). In this paper, we present a new concept of Js multiplicative metric space that covers different spaces including multiplicative metric space, multiplicative b-metric space and multiplicative b-metric-like space. Also we prove Ciric type fixed point theorem and some fixed point theorems with partial order in Js multiplicative metric space. 2. Js Multiplicative Metric Space Definition 2.1 Let ≠ ϕ  and let : [1, ) Ψ × → +∞   be a mapping. For all , ∈ w  we define the set ( ) , , Ψ B w  as follows: ( ) { } { } , , : lim ( , ) 1. →∞ Ψ = ⊂ Ψ = n n n B w w w w   Definition 2.2 Let ≠ ϕ  and : [1, ) Ψ × → +∞   be a given mapping. Then ( , ) Ψ  is called Js-multiplicative metric space, if it satisfies the following conditions: ( ) 1 Ψ For all , , ∈ wy  we have ( ) , 1 Ψ > wy and ( ) , 1 ; Ψ = ⇒ = wy w y ( ) 2 Ψ For all , , ∈ wy  we have ( ) , (, ); Ψ =Ψ wy yw ( ) 3 Ψ there exists 0 > h such that if for all ( ) , , ∈ × wy   { } ( ) , , , ∈ Ψ n w B w  then ( , ) lim sup ( , ). →∞ Ψ ≤ Ψ h n n wy w y The pair ( , ) Ψ  is called a Js multiplicative metric space. Remark 2.3 Clearly if the set ( , , ) Ψ B w  is empty for all , ∈ w  then ( , ) Ψ  is a Js multiplicative metric space if and only if ( ) 1 Ψ and ( ) 2 Ψ are satisfied. Example 2.4 Let [0, ) = +∞  and let : [1, ) Ψ × → ∞   be define by 2 ( ) ( , ) , + Ψ = w y wy α where 1 > α be a finite fixed real number is a Js multiplicative metric space for all , , . ∈ wy  Let ( ) , , , ∈ Ψ n z B w  then lim ( , ) 1. →∞ Ψ = n n z w So <∞ n z except possibly for finite number of terms. Let p be the smallest natural number such that , <∞ n z then