The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequalities which are more generalized than the inequalities of Dragomir and Cerone. The current article obtains bounds for the deviation of a function from a combination of integral means over the end intervals covering the entire interval. Some new purterbed results are obtained. Application for cumulative distribution function is also discussed.

In this paper, the notion of m-preinvex and ða; mÞ-preinvex functions is introduced and then several inequalities of Hermite-Hadamard type for differentiable m-preinvex and ða; mÞ-preinvex functions are established.

The aim of this manuscript is to establish common fixed points results for multi-valued mappings via generalized rational type contractions in complete b-metric spaces. Using the derived results, existence of solutions to certain integral equations and fractional differential equations in the frame of Caputo fractional derivative are studied. Examples are provided for the authenticity of the presented work.INDEX TERMS Common fixed points, b-metric space, set valued mappings, generalized rational type contraction, system of integral equation.

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