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The intent of this paper is to introduce the concept of Gb-cone metric and we describe some basic properties of such metric. Further, we establish some fixed point theorems for self-mappings satisfying the contractive type conditions and a common fixed theorem for two weakly compatible self-mappings satisfying the contractive condition in Gbcone metric spaces without the assumption of normality. Moreover, some examples are provided to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a common fixed point theorem by employing the notion of g -reciprocal continuity in probabilistic metric space. We demonstrate that g -reciprocal continuity ensures the existence of common fixed point under strict contractive conditions, which otherwise do not ensure the existence of fixed points. [ABSTRACT FROM AUTHOR]

In this paper, we prove some common fixed point theorems for a pair of weakly compatible mappings satisfying (Ψ, α, β)-weak contractions in fuzzy metric spaces employing a control function. Our results improve and generalize several previously known relevant results of the existing literature. Some illustrative examples are alsofurnished to substantiate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study the concept of soft semi-I-open sets with respect to an ideal. Then using these sets, we also study soft semi-I-continuous functions, soft semi-I-open functions and obtained some characterizations and several properties concerning these functions. [ABSTRACT FROM AUTHOR]