Some coincidence point results for generalized ( ψ , φ ) -weakly contractions in ordered b-metric spaces

Abstract

In this paper we present some coincidence point results for four mappings satisfying generalized (ψ , ϕ)-weakly contractive condition in the framework of ordered b-metric spaces. Our results extend, generalize, unify, enrich, and complement recently results of Nashine and Samet (Nonlinear Anal. 74:2201-2209, 2011 and Shatanawi and Samet (Comput. Math. Appl. 62:3204-3214, 2011). As an application of our results, periodic points of weakly contractive mappings are obtained. Also, an example is given to support our results. MSC: 47H10; 54H25

Contractive conditions in b-metric spaces

“…199-215), (Piri & Kumam, 2016), (Roshan et al, 2014a, pp. 725-737), (Roshan, et al, 2015), (Roshan et al, 2014b, pp. 613-624), (Sarwar et al, 2017, pp.…”

Coincidence point results via generalized (ψ,ϕ)-weak contractions in partial ordered b-metric spaces with application

“…For Example 3 of [20] it is easy to see that all conditions of our Theorem 2.1 are satisfied and hence the corresponding conclusions holds. However, if 1 < < 5 2 , then condition (1.1) of Theorem 1.10 does not hold for Example 2.9 but our condition (2.1) holds, therefore our Theorem 2.1 is a genuine generalization of Theorem 1.10.…”

“…In [20], the authors proved the following theorem with M(x, y) define by for all x, y ∈ X. Theorem 1.10. Let (X, , d) be a partial ordered complete b-metric space and f, g, R, S : X → X be four mappings such that f(X)⊆R(X) and g(X)⊆S(X).…”

“…In this direction fixed point results, coincidence point results and their application to the solution of linear and nonlinear integral equations are investigated (see [3,4,[19][20][21] and the reference cited therein).…”

Ordered b-metric spaces and Geraghty type contractive mappings

“…The following example shows that, in general, a b-metric does not necessarily need to be a metric, see also (Aghajani, et al, 2014), (Abbas, et al, 2016(Abbas, et al, , pp.1413(Abbas, et al, -1429, (Ansari, et al, 2016), (Ding, et al, 2016, pp.151-164), (Djukić, et al, 2011), (Huang, et al, 2015a, pp.808-815), (Huaping, et al, 2015), (Huang, et al, 2015b, pp.800-807), (Hussain, et al, 2012), (Hussain, et al, 2013), (Jleli, et al, 2012, pp.175-192), (Jovanović, et al, 2010), (Kadelburg, et al, 2015, pp.57-67), (Khamsi, Hussain, 2010, pp.3123-3129), , (Roshan, et al, 2015), (Roshan, et al, 2014, pp.229-245), (Zabihi, Razani, 2014 (Aghajani, et al, 2014, pp.941-960), (Abbas, et al, 2016(Abbas, et al, , pp.1413(Abbas, et al, -1429, (Ansari, et al, 2016), (Djukić, et al, 2011), (Huang, et al, 2015a, pp.808-815), (Huaping, et al, 2015), (Huang, et al, 2015b, pp.800-807), (Hussain, et al, 2012), (Hussain, et al, 2013), (Jleli, et al, 2012, pp.175-192), (Jovanović, et al, 2010), (Kadelburg, et al, 2015, pp.57-67), (Khamsi, Hussain, 2010, pp.3123-3129), , (Roshan, et al, 2015), (Roshan, et al, 2014, pp.229-245), (Zabihi, Razani, 2014) and the references mentioned therein. Also, for the concepts such as partial order, comparable, well ordered, nondecreasing, increasing, dominated, dominating and other, w...…”