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Some new classes of general harmonic convex sets and convex functions are introduced and studied in this paper. The optimality criteria of the differentiable general harmonic functions is characterized by the general harmonic variational inequalities. Special cases are also pointed out as applications of the new concepts. Auxiliary principle technique involving an arbitrary operator is applied to suggest and analysis several inertial type methods are suggested. Convergence criteria is investigated of the proposed methods under weaker conditions. The results obtained in this paper may inspire further research along with implementable numerical methods for solving the general harmonic variational inequalities and related optimization problems. [ABSTRACT FROM AUTHOR]

In this article, we define a generalized q-integral operator on multivalent functions. It generalizes many known linear operators in Geometric Function Theory (GFT). Inclusions results, convolution properties and q-Bernardi integral preservation of the subclasses of analytic functions are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate some new classes of mixed harmonic directional variational inequalities. Several important new problems are obtained as special cases. The auxiliary principle technique is applied to suggest and analyze some hybrid inertial iterative methods for solving the mixed harmonic directional variational inequality. The convergence analysis of these iterative methods is also considered under some mild conditions. Some special cases are also pointed out. Results proved in this paper can be viewed as a significant refinement and improvement of the known results. [ABSTRACT FROM AUTHOR]

Let 풜 be the class of normalized functions which are analytic in the open unit disc. Jakson q-derivative represented by convolution operator D q f (z) = 1 z { f (z) ★ z (1 - q z) (1 z) } , f ∈ 풜 , q ∈ (0 , 1) is used to introduce a unified class Mq(α, β, γ), α ≥ 0, β, γ ∈ [0, 1) and its various mapping properties are studied. For q → 1−1, β = γ = 0 and α = 1, this class reduces to the class K of close-to-convex univalent functions. A number of interesting results such as q-Bernardi integral operator and inclusion relations are included as part of this study. Applications are also pointed out as consequences of the main results. [ABSTRACT FROM AUTHOR]

Strongly Janowski functions are used to define certain classes of analytic functions which generalize the concepts of close-to-convexity and bounded boundary rotation. Coefficient results, a necessary condition, distortion bounds, Hankel determinant problem and several other interesting properties of these classes are studied. Some significant well known results are derived as special cases. [ABSTRACT FROM AUTHOR]

In this paper, some new classes of exponentially general nonconvex variational inequalities are introduced and investigated. Several special cases are discussed as applications of these nonconvex variational inequalities. Projection technique is used to establish the equivalence between the non- covex variational inequalities and fixed point problem. This equivalent formulation is used to discuss the existence of the solution. Several inertial type methods are suggested and analyzed for solving ex- ponentially general nonconvex variational inequalities. using the technique of the projection operator and dynamical systems. Convergence analysis of the iterative methods is analyzed under suitable and appropriate weak conditions. In this sense, our result can be viewed as improvement and refinement of the previously known results. Our methods of proof are very simple as compared with other techniques. [ABSTRACT FROM AUTHOR]