The concepts of generalized higher derivations, Jordan generalized higher derivations, and Jordan generalized triple higher derivations on Γ-ring M into ΓM-modules X are presented. We prove that every Jordan generalized higher derivation of Γ-ring M into 2-torsion free ΓM-module X, such that aαbβc=aβbαc, for all a, b, c M and α,βΓ, is Jordan generalized triple higher derivation of M into X.

This paper deal with the estimation of the shape parameter (a) of Generalized Exponential (GE) distribution when the scale parameter (l) is known via preliminary test single stage shrinkage estimator (SSSE) when a prior knowledge (a₀) a vailable about the shape parameter as initial value due past experiences as well as suitable region (R) for testing this prior knowledge.

The Expression for the Bias, Mean squared error [MSE] and Relative Efficiency [R.Eff(×)] for the proposed estimator are derived. Numerical results about beha

Despite ample research on soft linear spaces, there are many other concepts that can be studied. We introduced in this paper several new concepts related to the soft operators, such as the invertible operator.  We investigated some properties of this kind of operators and defined the spectrum of soft linear operator along with a number of concepts related with this definition; the concepts of eigenvalue, eigenvector, eigenspace are defined. Finally the spectrum of the soft linear operator was divided into three disjoint parts.

     This article is devoted to presenting results on invariant approximations over a non-star-shsped weakly compact subset of a complete modular space by introduced a new notion called S-star-shaped with center f:  if   be a mapping and , . Then the existence of common invariant best approximation is proved for Banach operator pair of mappings by combined the hypotheses with Opial’s condition or demi-closeness condition

In this article, the additivity of higher multiplicative mappings, i.e., Jordan mappings, on generalized matrix algebras are studied. Also, the definition of Jordan higher triple product homomorphism is introduced and its additivity on generalized matrix algebras is studied.

In this paper, new concepts which are called: left derivations and generalized left derivations in nearrings have been defined. Furthermore, the commutativity of the 3-prime near-ring which involves some
algebraic identities on generalized left derivation has been studied.

Let M be ,-ring and X be ,M-module, Bresar and Vukman studied orthogonal
derivations on semiprime rings. Ashraf and Jamal defined the orthogonal derivations
on -rings M. This research defines and studies the concepts of orthogonal
derivation and orthogonal generalized derivations on ,M -Module X and introduces
the relation between the products of generalized derivations and orthogonality on
,M -module.

          The present paper studies the generalized Φ-  recurrent of Kenmotsu type manifolds. This is done to determine the components of the covariant derivative of the Riemannian curvature tensor. Moreover, the conditions which make Kenmotsu type manifolds to be locally symmetric or generalized Φ- recurrent have been established. It is also concluded that the locally symmetric of Kenmotsu type manifolds are generalized recurrent under suitable condition and vice versa. Furthermore, the study establishes the relationship between the Einstein manifolds and locally symmetric of Kenmotsu type manifolds.