FIXED POINT THEOREMS IN MENGER SPACES USING THE $(CLR_{ST})$ PROPERTY AND APPLICATIONS

MOHAMMAD  IMDAD; B. D.  PANT; SUNNY  CHAUHAN

FIXED POINT THEOREMS IN MENGER SPACES USING THE $(CLR_{ST})$ PROPERTY AND APPLICATIONS

Authors

MOHAMMAD IMDAD Department of Mathematics, Aligarh Muslim University, Aligarh-202 002, Uttar Pradesh, India
B. D. PANT Government Degree College, Champawat-262 523, Uttarakhand, India
SUNNY CHAUHAN Near Nehru Training Centre, H. No. 274, Nai Basti B-14, Bijnor-246 701, Uttar Pradesh, India

Keywords:

t-norm, Menger space, Weakly compatible mappings, (E.A) property, Common property (E.A), (CLRS) property, (CLRST) property, Fixed point

Abstract

In the present paper, we prove a common fixed point theorem for two pairs of weakly compatible mappings in Menger space employing the $(CLR_{ST})$ property. Some examples are furnished which demonstrate the validity of the hypotheses and degree of generality of our results. We extend our main result to four finite families of self mappings. As applications to our results, we obtain the corresponding common fixed point theorems in metric spaces. Our results improve and extend the results of Cho et al. [4] and Pathak et al. [21] besides several known results.