In this paper, we study some unique coupled coincidence points for rational type contractions involving generalized altering distance functions in metric spaces. Our results unify and generalize various known comparable results from the current literature, Gupta et. al. [15], Nashine and Aydi [21], Rashwan and Saleh [25] and many known results. An example is also given to support our main results.

In this paper, some coupled coincidence and common fixed 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 fixed point theorems which contain altering distance functions may be obtained. Our results can be applied directly to study multidimensional fixed point theorems which cover the concepts of coupled , tripled, quadruple fixed point etc.

In present paper we introduce the concepts of mixed g-monotone property and \Delta_g-symmetric property, where g is single valued mapping, for multi-valued mapping under any number of variables and use it to obtain some existence and uniqueness fixed points for hybrid pair of mappings under general contractive conditions in partially ordered metric spaces. Our results are generalizations of several results in this direction. We equipped this paper with examples in order to illustrate the effectiveness of our generalizations.

The aim of this work is to obtain some existence and uniqueness fixed point theorems for mixed g-monotone
mapping in any number of variables under general contractive conditions in partially ordered metric spaces by using the condition of weak compatibility. Our results are different, more natural and generalizations of many results on multidimensional fixed points. For illustration of the effectiveness of our generalizations, some examples are equipped in this paper.

In this paper, we establish a common fixed point theorem for two pairs of mappings satisfying an almost generalized contractive condition for comparable elements in a partially ordered metric space. Our results generalize and extend the main results in [2] to multi-valued mappings. As corollaries we obtain the results in [8, 9], and many others.

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 prove some xed point theorems in 2-Menger space under new contraction
conditions.

In this paper we prove some common fixed point theorems for family of occasionally weakly compatible mappings in Menger space. Also improvement of the results of B. D. Pant and Sunny Chauhan [1] under relaxed conditions is given.

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].

The aim of this work is to demonstrate various an interesting recursion formulas, differential recursion formulas, differential operators, integral operators, integration formulas, and generating relations for each of Horn's hypergeometric functions , , , , ,  and  by the contiguous relations of Horn's hypergeometric series. Some interesting special cases of our main results are also constructed.