Browsing by Author "Babalola, Kunle Oladeji"
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Item Analytic functions defined by expressions having geometric meaning(Element d.o.o., Zagreb, Croatia, 2017) Jimoh, F. M.; Babalola, Kunle OladejiWe define a new class J_n^α (β) of analytic functions by a product of certain expressions having geometric meaning. We establish univalence of the new class, obtain its integral representations, sufficient inclusions conditions and coefficient inequalities. Examples are givenItem Bounds on coefficients of certain analytic functions(Faculty of Science, University of Ilorin, Ilorin, Nigeria, 2013) Jimoh, F. M.; Ganiyu, M. A.; Ejieji, C. N.; Babalola, Kunle OladejiIn this paper, we obtain bounds on some early coefficients of analytic functions which have the form f(z)=z+a_2 z^2+⋯ and which satisfy certain geometric conditionsin the open unit disk E={z∈ C:|z|<1}Item Bounds on coefficients of certain analytic functions(Faculty of Science, University of Ilorin, Ilorin, Nigeria, 2013) Jimoh, F. M.; Ganiyu, M. A.; Ejieji, C. N.; Babalola, Kunle OladejiIn this paper we obtain bounds on some early coefficients of analytic functions which have the form f(z)=z+a_2z^2+...and satisfy certain geometric conditions in the unit disk E = {z: |z|<1}.Item Bounds on the coefficients of certain analytic and univalent functions(Romanian Academy, Romania, 2008) Babalola, Kunle OladejiFor the real number α>1, we use a technique due to Nehari and Netanyahu and an application of certain integral iteration of Caratheodory functions to find the best-possible upper bounds on the coefficients of functions of the class T(_n^α)(β) introduced in [4] by OpoolaItem Coefficient bounds for certain Bazilevic maps(Romanian Academy, Romania, 2017) Sidiq, M; Babalola, Kunle OladejiFollowing Babalola [3] we obtain the best possible upper bound for the coefficients of functions in the class B_n^λ (γ) using a technique due to Nehari and Netanyahu [9] and an application of certain integral iteration of Caratheodory-type functions. The sharp bound on the Fekete-Szego functional in B_n^λ (γ) is also obtainedItem Coefficient determinants involving many Fekete-Szego-type parameters(Canadian University of Dubai, Dubai, United Arab Emirate, 2015) Babalola, Kunle OladejiWe extend our definition (in a recent paper [3]) of the coefficient determinants of analytic mappings of the unit disk to include many Fekete-Szego-type parameters, and compute the best possible bounds on certain specific determinants for the choice class of starlike functionsItem Coefficient estimates for certain classes of analytic functions(Nigerian Mathematical Society, 2014) Ganiyu, M. A.; Jimoh, F. M.; Ejieji, C. N.; Babalola, Kunle OladejiBounds on early coefficients of analytic functions normalized by f(0)=f^'(0)-1=0 which satisfy Re (〖f(z)〗^(α-1) f^' (z))/z^(α-1) (1+(zf^'' (z))/(f^' (z) ))>0 in the unit disk U ={z∈ C:|z|<1} are obtained using known properties of functions with positive real partItem Combinations of geometric expressions implying schlichtness.(Department of Mathematics, Faculty of Science, University of Oradea, Romania, 2014) Babalola, Kunle OladejiIn this short paper we prove an interesting result that certain not-linear combinations of geometric expressions of the form φ(f,f^',f^'' )+λϕ(f,f^',f^'') imply schlichtness of holomorphic functions, normalized by f(0) and f^' (0)=1, in the unit disk E={z∈ C:|z|<1}Item Convex null sequence technique for analytic and univalent mappings of the unit disk(Tamkang University, 2009) Babalola, Kunle OladejiIn this paper, we employ a technique based on the convex null properties of certain infinite sequences to study various classes of analytic and univalent functions in the open unit disk. The technique simplifies many problems of the theory of geometric functions and our results generalize and extend many earlier onesItem Cousins of the Bernoulli Inequality(Faculty of Science, University of Ilorin, Ilorin, Nigeria, 2012) Babalola, Kunle Oladeji; Ejieji, C. N.We present elementary inequalities of Bernoulli type, which have applications in the theory of inequalities, especially the geometric function theoryItem Cousins of the Bernoulli Inequality(Faculty of Science, University of Ilorin, Ilorin, Nigeria, 2012) Babalola, Kunle Oladeji; Ejieji, C. N.We present elementary inequalities of the Bernoulli type, which have applications in the theory of inequalities, especially the geometric functions theory.Item Early coefficients of close-to-star functions of type alpha(Nigerian Mathematical Society, 2012) Babalola, Kunle Oladeji; Olasupo, A. O.; Ejieji, C. N.We obtain sharp bounds on the early coefficients of certain close-to-star analytic functions of type α in the unit disk E ={z∈ C:|z|<1}Item The fifth and sixth coefficients of α-close-to-convex functions(Faculty of Science, University of Kragujevac, Serbia, 2009) Babalola, Kunle OladejiWe obtain sharp bounds on the fifth and sixth coefficients of α-close-to-convex functions introduced in [2]Item Functions defined by products of geometric expressions(Mathematical Association of Nigeria, 2015) Jimoh, F. M.; Babalola, Kunle OladejiWe introduce a new class of analytic and univalent functions defi ned by product of geometric expressions. The univalence of functions in the new class as well as sufficient inclusion condition is established. The radius of convexity for the class is also obtained.Item A generalization of starlikeness condition(Nigerian Mathematical Society, 2016) Ejieji, C. N.; Babalola, Kunle OladejiIn this paper, we prove a generalization of a well known starlikeness condition in the unit disk using a method of linear combinations of certain geometric expressions. Some interesting corollaries are mentionedItem Integral means of analytic mappings by iteration of Janowski functions(University of Shomal, Amol, Iran, 2010) Babalola, Kunle OladejiIn this short note we apply certain iteration of the Janowski function to estimate the integral means of some analytic and univalent mappings of |z|<1. Our method of proof follows an earlier one due to Leung [4]Item Iterated integral transforms of Caratheodory functions and their applications to analytic and univalent functions(Tamkang University, 2006) Babalola, Kunle Oladeji; Opoola, T. O.In this paper, we develop and study some integral transforms of Caratheodory functions. We apply the transforms to study certain other classes of analytic and univalent functions both to obtain new results and provide new proofs of some known onesItem New generalizations of Bazilevic maps(Element d.o.o., Zagreb, Croatia, 2016) Babalola, Kunle OladejiIn this work we study via Caratheodory maps with normalization by other than unity, a generalization of certain well-known subfamily of Bazilevic functions using the also well-known Salagean derivative operatorItem New insights into Bazilevic maps(Department of Mathematics, Faculty of Science, University of Oradea, Romania, 2016) Babalola, Kunle OladejiThe well-known family of Bazilevic maps are studied via a class of Caratheodory type analytic functions normalized by other than unity. The results are groundbreaking, especially that they concern this great class as a wholeItem New subclasses of analytic and univalent functions involving certain convolution operators(Romanian Academy, Romania, 2008) Babalola, Kunle OladejiLet E be the open unit disk {z∈ C:|z|<1}. Let A be the class of analytic functions in E which have the form (z)=z+a_2 z^2+⋯ . We define operators L_n^σ:A→A using the convolution *. Using these operators, we define and study new classes of functions in the unit disk. Moreover, we obtain some basic properties of the new classes, namely inclusion, growth, covering, distortion, closure under certain integral transformation and coefficient inequalities
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