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In this paper, we prove some common fixed point results for four mappings satisfying generalized contractive condition in S-metric space. Our results extend and improve several previous works.

Banach Contraction Principle (BCP) is a fundamental result in metric fixed point theory and it is a very powerful tool in solving the existence problems in pure and applied sciences. Also, the fuzzy set theory has many applications in various branches of engineering, mathematical sciences including artificial intelligence, control engineering, computer science, management science etc., see [1]. The aim of this paper is to study a common fixed point results for fuzzy mappings under implicit relation in a complex-valued metric space. we introduces a new class of an implicit relation to prove a common fixed point theorems for fuzzy mappings in this paper and constructed some examples to illustrate the main theorem. Also, we gave the consequences of our main result. The results have been reached in our current research work that consider applying for an integral0type0contractive0condition, these 0results0are 0extention0 ofnmanyw resultszinz thiszfield.

Tuberculosis is a prevalent public health problem especially in the poor developing countries and results in significant mortality. Albeit tuberculosis almost always affects any organ or system of the body, abdominal tuberculosis is less frequent; moreover, tuberculous appendicitis is very rare with an incidence estimated at about 0.1–0.6% of all gastrointestinal tuberculosis. The purpose of this report was to present an unusual case of primary tuberculous appendicitis and the approach used for accurate diagnosis as well as a current update on the disease. We are reporting a 30-year-old male who presented with acute abdominal pain, fever, and vomiting and was admitted with the clinical diagnosis of acute appendicitis. Patient was investigated thoroughly and histopathologic examination was strongly suggestive of tuberculous appendicitis; however, Ziehl-Neelsen (ZN) was negative in tissue section. To confirm the diagnosis, molecular biology [polymerase chain reaction (PCR)] study was performed from the formalin fixed paraffin embedded (FFPE) appendicular tissue and revealed presence of Mycobacterium tuberculosis. As there are numerous differential diagnoses in granulomatous lesions of appendix and due to the fact that appendicular tuberculosis is a rare phenomenon; verification etiologic agent is crucial for appropriate management of the disease.

In this paper we define a new class of hyperholomorphic functions, which is known as F α G (p, q, s) spaces. We characterize hyperholomorphic functions in F α G (p, q, s) space in terms of the Hadamard gap in Quaternion analysis.