In this paper, some coupled coincidence and common xed point theorems for two self mappings have been derived which satisfy certain inequality involving a function of two variables that measures the distance between points in ordered metric spaces. For particular choices of the function several generalizations of many xed point theorems which contain altering distance functions may be obtained. Our results can be applied directly to study multidimensional xed point theorems which cover the concepts of coupled , tripled, quadruple xed point etc.

In this paper, we prove some xed point theorems in 2-Menger space under new contraction conditions.

In this paper we prove a common fixed point theorem for six compatible self mappings of type (A) in a complete non-Archimedean Menger PM-space.

In this paper, we show that some results of Sharma and Deshpande [19] are not valid, we also give supporting example. Finally, we consider the concept of weakly compatible mappings to improve the main result of Pathak [9].

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The aim of this paper deals with the study of the Horn matrix function of two complex variables. The convergent properties, an integral representation of H2(A,A′,B,B′;C;z,w) is obtained and recurrence matrix relations are given. Some result when operating on Horn matrix function with the differential operator D and a solution of certain partial differential equations are established. The Hadamard product of two Horn’s matrix functions is studied, certain results as, the domain of regularity, contiguous functional relations and operating with the differential operator D and D2 are established.

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DFT with B3LYP/6-311++G(d,p) level were used for all calculations in this work. In biological system, 5-FU- 3H2O has the highest stabilization energy compared to 5-FU- 3NH3, 5-FU dimer, and 5-FU monomer. The chemical interactions of 2′-deoxyribose radical with uracil and 5-FU radicals to form 2′-deoxyuridine and 2′-deoxy-5-fluorouridine show that the difference in stabilization energies, ΔE, for their formation are quite low which facilitates the exchange reactions in DNA structure. Size, shape density distributions, and chemical reactivity sites of 5-FU were obtained by mapping electron density isosurface with electronic surface. Additionally, the intermolecular hydrogen bonding in 5-FU (sugarphosphate) backbone system was simulated by NBO analysis to describe the role of intermolecular hydrogen bonding on the structure and chemical reactivity of 5-FU in biological systems. Molecular docking study of the interaction between 5- FU and human serum albumin (HSA) indicated that 5-FU binds to HSAwith low affinity and low specificity compared to other anticancer drugs.