(α, β)-Zb-GERAGHTY TYPE CONTRACTION IN b-METRIC-LIKE SPACES VIA b-SIMULATION FUNCTION

(α, β)-Z_bGERAGHTY TYPE CONTRACTION IN b-METRIC-LIKE SPACES VIA b-SIMULATION FUNCTION

S. NEGI, S. ANTAL, U. C. GAIROLA

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Abstract. The aim of this paper is to introduce the notion of (α,β)-Z_b-Geraghty type contraction via b-simulation function and use this contraction to establish a common fixed point theorem for a pair of self-mappings in the context of a b-metric-like space. Our result extends and generalizes the result of Matthews [21], Khojasteh et al. [20], Demma et al. [15], Chandok [12] and some others also. We deduce some corollaries from our main result and provide examples to illustrate our results. Moreover, we apply our result to obtain a solution of second order differential equation.

Keywords:Common fixed point, b-metric-like space, (α, β)-Z_b-Geraghty type contrac- tion, b-simulation function.

AMS Subject Classification: 47H10, 54H25.